Crushing apparatus of the type mentioned above has already been proposed by the applicants (German Patent Application No. P 37 12 147.2). According to this a size reduction device which can be constructed in the form of a hammer mill, an impact mill, a mixing vessel with fluid supply or in any other suitable manner is arranged in the region between a roller mill and screen classifier in order to reduce the size of the flat round agglomerates (so-called scabs) formed in the pressure crushing before the classifying operation so as to release the fines contained in these agglomerates. Crushing apparatus of this type is particularly suitable for pressure crushing of mineral material for grinding, such as for example cement clinker and ore. This crushing can generally take place in a dry or wet process.